Dimension Of Cantor Function Non-differentiable Point Set

Fractal geometry has rapidly developed into a new branch of mathematics in the past three decades,and its theory has been widely used in many fields.In 1883,Cantor,a German mathematician,put forward the Cantor set.The construction of the classic middle-third Cantor set is very simple.However,it can reflect the most typical char-acteristics of fractal geometry,We can calculate the Hausdorff dimension of the classic middle-third Cantor set as log 2/log 3.As for the classic middle-third Cantor set,our re-search is not limited to the initial measure calculation and the proof of dimension.In fact,many scholars have done a lot of in-depth research on the jobs of the non differentiable points of Cantor function in 1993,Darst[24]proves that the Hausdorff dimension of the set of nondifferentiable points of Cantor function of the classic middle-third Cantor set is?log 2/log 3?²,and points out that this conclusion can be extended to the general Cantor function.Eidswick points out that the Cantor function of the classic middle-third Cantor set is characterized by the interval between 0 and 2 in the three progressive formulas,It is also proved that the potential of a subset T_??of the set of nondifferentiable points of Cantor function is a continuum,and the subset T_??is a more precise characterization of differential properties.Therefore,we can further calculate the Hausdorff dimension and packing dimension of the set T_??.